Biophysics Biological soft matter

Transcription

1 Biophysics Biological soft matter!"#$%&'(&)%*+,-.& /"#$%("%*+,-.0."122,13$(%4(5+&

2

3 Biophysics lectures outline Biological soft matter 1. Biopolymers 2. Molecular motors 3. The cytoskeleton

4 Biophysics 1. Biopolymers!"#$%&'(&)%*+,-.& /"#$%("%*+,-.0."122,13$(%4(5+&

5 DNA

6 Born 1920 London Died of cancer 1958 (age 37) Rosalind Franklin

7 James Watson and Francis Crick Cavendish Cambridge 1953

8 Rosalind Franklin!s x-ray diffraction data Shown to James Watson by her colleague Maurice Wilkins without her permission or knowledge

9 DNA

10 DNA

11 DNA by AFM AFM of DNA (Andy Lee PhD student with Jamie Hobbs)

12 6/#71,-8&9/%-.4/,:7,#-&2%47#/& Lac repressor

13 Protein Myoglobin

14 @133&<,#:#3AB1/.& ;,4/#75<531.& =47,-& >?=&

15 =47,-&

16 =47,-&

17 ;,4/#75<531.&

18 ;,4/#75<531.&

19 ;,4/#75<531.&

20 ;,4/#75<531.&

21 ;,4/#75<531.&C&B,7#7,4&.:,-$31&

22 Experiments on a single DNA chain

23 Attaching DNA to a surface and a bead /STREPTAVIDINE

24 Magnetic Tweezers

25 Optical Tweezers

26 Stretching DNA film-dna-stretch

27 Stretching DNA Breaking of a DNA molecule due to stretching by flow

28 Force extension curve for DNA (Storm & Nelson 2003) DNA-B DNA-S

29 Force extension curve for different models for DNA Chaîne d!ising 1D Semi-flexible model Chaîne semi-flexible 3D

30 Random walk 2D on square lattice

31

32 Biophysics 2. Molecular Motors!"#$%&'(&)%*+,-.& /"#$%("%*+,-.0."122,13$(%4(5+&

33 Molecular motors! Observation kinesin on microtubule (Block, Stanford) Observation dynein on microtubule (Vale, UCSF):

34 Proteins

35 =B,-#&%4,$.& Don t occur in natural proteins

36 (hydrophobic) (hydrophilic) (hydrophilic, polar positively charged) (hydrophilic, polar negatively charged) Don t occur in natural proteins =B,-#&%4,$.& D/1.,$51.E&

37 ;#31453%/&,-71/%47,#-.&! Covalent (harmonic) k(x x 0 ) 2! Ionic (Coulomb)! van der Waals q 1 q 2 ɛ r A r 12 B r 6! Hydrogen bonds! Hydrophobic

38 9"1&)A$/#:"#<,4&F22147&!"#$ %&'()$! F-7/#:,4&4#.7&#2&#/$1/,-G&*%71/&! 6##/3A&5-$1/.7##$&

39 co-ion bound counterion diffuse counterion Poisson-Boltzmann equation: d 2 V dx 2 = zeρ 0 ɛɛ 0 e zev k B T! ;,-,B,.1&1-1/GA8&.7%A&43#.1&<A&! ;%J,B,.1&1-7/#:A8&$,225.1&%*%A&! &&&&&&&4#5-71/,#-&43#5$&

40 6/#71,-&L7/5475/1& Primary Secondary Tertiary Quaternary A G V S Y G G Q P R F A L )A$/#:"#<,4&/1.,$51.&,-.,$1K& "A$/#:",3,4&/1.,$51.&#-&.5/2%41&

41 L14#-$%/A&L7/5475/18&%3:"%&"13,41.&

42 L14#-$%/A&L7/5475/18&<17%&."117.& Parallel!-sheet Anti-parallel!-sheet

43 ;1B</%-1&6/#71,-.& Alamethicin ~ a voltage gated ion channel

44 6/#71,-&M#3$,-G&C&2/11&1-1/GA& "G "G fold

45 6/#71,-&M#3$,-G&H&N1O,-7"%3P.&:%/%$#J&! Number of possible configurations > ! If sample all to fold would take > universe age! Proteins fold in ~ milliseconds

46 6/#71,-&M#3$,-G&3%-$.4%:1&

47 ;#31453%/&/14#G-,7,#-&

48 ;#31453%/&/14#G-,7,#-&H&7"1/B#$A-%B,4.& G = U T S Electrostatics, H-bonds, van der waals Vibrational entropy, hydrophobic effect G < 0 for binding to occur

49 Molecular motors! Observation kinesin on microtubule (Block, Stanford) Observation dynein on microtubule (Vale, UCSF):

50 ;#$133,-G&B#31453%/&B#7#/.&.71::,-G& ;%.71/&1R5%7,#-.&2#/&:/#<%<,3,7A&$A-%B,4.&& k L! k R! Q& n-1! n! n+1! P n t = k R (P n 1 P n ) + k L (P n+1 P n ).

51 Molecular motors! Bind to polymer filaments! Walk along filaments! Bind to 2 filaments! exert stress Molecular motors: myosin + actin "! contractility

52 ATP synthase

53

54

55 DNA polymerase: film-enzyme

56 Polymerisation of filaments k on k off

57 %47,-& barbed/plus end + - pointed/minus end

58 B,4/#75<531.& ST-B&

59 ;,4/#75<531&$A-%B,4.&

60 9/1%$B,33,-G&

61 6#3AB1/,.%7,#-&1J1/7,-G&%&2#/41& k on F!

62

63 Biophysics 3. The Cytoskeleton!"#$%&'(&)%*+,-.& /"#$%("%*+,-.0."122,13$(%4(5+&

64 What is the cytoskeleton made of?! Cytoskeleton proteins! Microtubules + actin + intermediate filaments! Polymerise into filaments! Crosslinks - polymer gel! Molecular motors! Other proteins - MAPs (microtubule associated proteins) - ABPs (actin binding proteins) Cytoskeleton polymers: microtubules + actin

65 What type of material is the cytoskeleton?! Continuum level description! Soft matter! Viscoelastic! Out of equilibrium! Active matter

66 Where does a cell s energy come from?! photosynthesis/ respiration! ATP + H 2 O! ADP + P i! energy!

67 9%+1.&,-&",G"&#/$1/&1-1/GA&D-1G%7,O1&1-7/#:AE& FJ:13.&$,.#/$1/&D*%.71E&1(G(&"1%7&!

68 U,.4#13%.7,4&G13! Maxwell linear model:! 2ηu ij = strain rate! ( 1 + τ D Dt ) σ ij stress! Viscous fluid part:! 2ηu ij = σ ij viscosity! Elastic part:! 2Eɛ ij = σ ij Youngs modulus! Hooke s law!

69 Low Reynolds number! Force balance in low Reynolds number:! i (σ ij P δ ij ) = 0 Re = ρvl η 1 viscous forces >> inertial forces!

70 Incompressibility! v = 0! Most fluids are incompressible!! Is the cytoskeleton incompressible?!

71 6#3%/W-1B%7,4&3,R5,$&4/A.7%3& solid nematic liquid crystal liquid polar $,.7#/7,#-&.7/1..&V& ν 2 (p αh β + p β h α ) 1 2 (p αh β p β h α )

72 6#3%/&3,R5,$&4/A.7%3& ν $,.7#/7,#-&.7/1..&V& 2 (p αh β + p β h α ) 1 2 (p αh β p β h α ) *"1/1&B#31453%/&2,13$& h = δf d δp M/%-+&$,.7#/7,#-&2/11&1-1/GA& F d = 1 K 1 ( p) 2 + K 2 [p ( p)] 2 + K 3 [p ( p)] 2 2 & & & &.:3%A & & & & &7*,.7 & & & && & &<1-$ && X-&#-1&4#-.7%-7&%::/#J,B%7,#-& & & & & & & &2#/& h = K 2 θ p = (cos θ, sin θ)

73 =47,O1&.7/1..& Chemical potential of ATP + H 2 O! ADP + P i Actomyosin contractile ζ < 0

74 Active polar fluid σ αβ = 2ηu αβ + ν 2 (p αh β + p β h α ) 1 2 (p αh β p β h α ) ζ µ(p α p β δ αβ 2 ) viscous stress distortion stress active stress ζ < 0! Actomyosin contractile! Polarisation p and conjugate molecular field h! Low Re steady state force balance (Cauchy) α (σ αβ P δ αβ ) = 0

75 Dynamics of the polarisation field p α t = (v γ γ )p α ω αβ p β νu αβ p β + 1 γ h α + λp α µ vorticity ω αβ = 1 2 ( αv β β v α ) rotational viscosity active

76 =47,O1&B%771/&%7&$,221/1-7&.4%31.&! Subcellular Cytoskeleton! Multicellular Tissues, Bacteria colonies! Multiorganism Flocks, Shoals, Herds

77 Conclusion on the cell cytoskeleton! Soft matter! Out of equilibrium active Cytoskeleton polymers: microtubules + actin

78 The Inner Life of a Cell animation created by NewTek LightWave 3D for Harvard Biovisions Conception and scientific content by Alain Viel and Robert A. Lue. Animation by John Liebler/XVIVO

79 Z##+&3,.7&! $1&[1--1.&I&6/#.7&!"#$%"&'()'$*+$,(-.(/$01&'234'$! $1&[1--1.&5)34(67$)*6)#82'$(6$8*4&9#1$8"&'()'&! 8"&'()'$! X./%13%4"O,3,&;62#19*4#).431$36/$'.1+3)#$+*1)#'&! =3<1/7.&17&%3&<*4#).431$=(*4*7&$*+$2"#$)#44$! 6",33,:.&17&%3&%"&'()34$=(*4*7&$*+$2"#$)#44$!?13.#-&>(*4*7()34$8"&'()'&

80 Important copyright disclaimer Please note that many of the images in these slides do not have the full citations or copyright licence numbers that they should have. These slides are shared with you for your learning purposes only. No image can be reproduced or shared without full copyright permission being sought.